The long-time chronoamperometric current at an inlaid disk electrode

Abstract

Existing analytical solutions for the long-time chronoamperometric current response at an inlaid disk electrode are restricted to diffusion-limited currents due to extreme polarisation or reversible kinetics at the electrode surface. In this article, we derive an approximate analytical solution for the long-time-dependent current when the kinetics of the redox reaction at the electrode surface are quasi-reversible and the diffusion coefficients of the oxidant and reductant are different. We also detail a novel method for calculating the steady-state current. We show that our new method encapsulates and extends the existing solutions, and agrees with numerically simulated currents.

Time-dependent chronoamperometric response of dual inlaid disk electrodes

“…The equivalent expression for the current through disk 2 can be obtained by interchanging the subscripts 1 and 2 in (60). We recall that the factor I ss (β) in the above expressions can be derived for 0 ≤ β ≤ 500 from the working curve in the Supplementary Data to our previous paper [18], and for β > 500 from the asymptotic expression (24) derived by Phillips [23]. We also emphasize that the percentage error in expression (60a) for the current is O(ǫ 3 ), i.e.…”

“…Since ǫ ≪ 1, there is an inner region near each disk where the concentrations are at steady-state to leading order, and an outer region where the concentrations are timedependent to leading order. We will find the solutions in both regions using matched asymptotics in a similar manner to the single-disk problem descibed in our previous article [18]. In the inner region near disk j, the coordinate system is (r j , z, θ j ) as defined above, and variables will be C O, j (r j , z, θ j , t) and C R, j (r j , z, θ j , t).…”

“…As in [18][19][20], the solution for χ(β; r, z) can be written in terms of the unknown flux through the boundary, q(β; r), as:…”

“…and it can be calculated using Tranter's method [22] to solve (19) in terms of a series of Bessel functions, as described in our previous article [18]; in that article, we also included in the Supplementary Data a working curve for I ss (β) for β in the range 0 ≤ β ≤ 500. For values of β > 500, I ss (β) can be calculated using the asymptotic expansion derived by Phillips [23] for large β:…”

“…We use Van Dyke's method [24] to find the leading-order impact in the far field of the leading-order inner solutions at the two disks. Writing the inner solutions C (18) in terms of the outer variablesr j andẑ, using the far-field behaviour of χ(β; r, z) given by (22), and letting ǫ tend to zero, we find that…”